Deformed Calabi-Yau Completions

Understand

We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories.

• Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras associated to quivers with potentials and dg categories associated to the category of coherent sheaves on the canonical bundle of a smooth variety.
• We show that deformed Calabi-Yau completions do have the Calabi-Yau property and that their construction is compatible with derived equivalences and with localizations.
• In particular, Ginzburg dg algebras have the Calabi-Yau property.